After teaching hundreds of engineers learn machine learning last 5 years, a pattern becomes hard to ignore.
Most people don’t struggle because machine learning is too difficult.
struggle because they start in the wrong place.
The usual path looks like this:
Take a crash course.
Import a framework.
Train a model.
Tune hyperparameters and move on.
They start with tools.
Frameworks. APIs. Pretrained models.
Everything works, until it doesn’t.
At first, progress feels fast.
You can reproduce a tutorial in an evening. You can train a model in an afternoon. You can get something into production surprisingly quickly.
And then, slowly, friction appears.
A model overfits.
A small data change breaks performance.
A colleague asks why a method works better than another.
A paper introduces a “simple” idea that somehow feels impossible to follow.
At that moment, many engineers quietly conclude:
“I’m not a math person.”
That conclusion is wrong.
What’s actually missing is structure.
**Machine learning is not a collection of tricks.
Linear algebra, probability, statistics, and optimization are not “prerequisites.”**
They are the language machine learning is written in.
Once that language is familiar, many things that seemed complex become obvious.
When you skip those layers, everything above them feels fragile and mysterious.
This is why so many ML practitioners:
Can train models but can’t explain them
Can follow tutorials but can’t adapt ideas
Can use tools but struggle to reason about failure modes
The solution is not learning more frameworks, libraries and tools.
It’s better foundations.
And contrary to popular belief, you don’t need:
- a PhD
- 5 more years of experience
- years of formal math training
What you need are the right books, written by people who understand how learning actually happens.
Books that:
- respect your time
- explain ideas before formalism
- connect math directly to algorithms
That’s what this list is about.
Below are 10 free, high-quality books that quietly do what most courses fail to do:
they help you understand machine learning, not just use it.
1.Mathematics for Machine Learning, A. Aldo Faisal, and Cheng Soon Ong
https://mml-book.github.io/book/mml-book.pdf
The gold standard for ML math: linear algebra, calculus, probability, clearly connected to algorithms.
2.Dive into Deep Learning, Cambridge University Press
A modern deep learning textbook with math, code, and intuition side-by-side.
3.Think Bayes by Allen B. Downey
https://allendowney.github.io/ThinkBayes2/
Bayesian reasoning explained through code and real examples.
**
4.Think Stats** by Allen B. Downey
https://greenteapress.com/thinkstats2/thinkstats2.pdf
Statistics for people who want to understand data, not memorize formulas.
5.Machine Learning from Scratch By Danny Friedman
https://dafriedman97.github.io/mlbook
Classic ML algorithms built step by step, no black boxes.
6.Patterns, Predictions, and Actions, M. Hardt and B Recht
https://mlstory.org/pdf/patterns.pdf
A conceptual ML book focused on generalization, optimization, and causality.
7.Mathematical Introduction to Deep Learning, A. Jentzen, B. Kuckuck, P. von Wurstemberger
https://arxiv.org/pdf/2310.20360
Neural networks explained from first principles.
**
8.Calculus, by Gilbert Strang, MIT Press**
https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_full_book.pdf
A book that will give you step by step foundation of Calculus.
**
9.Linear Algebra for Machine Learning**, by University of Pennsylvania.
https://www.cis.upenn.edu/~cis5150/linalg-I-f.pdf
The language of data, vectors, and transformations, made practical.
10.Mathematical Theory of Deep Learning
https://arxiv.org/pdf/2407.18384
For readers who want to understand how and why deep learning works under the hood.
Understanding accumulates quietly.
And once it’s there, it doesn’t disappear when the tools change.
Frameworks will be replaced.
APIs will evolve.
Terminology will shift.
The underlying ideas will not.
That’s why these books matter.
They are not about keeping up.
They are not trendy.
They are not optimised for clicks.
They are the kind of resources you come back to years later and think,“I finally see it now.”
And in a field that changes as quickly as machine learning, that turns out to be a long-term advantage.
If this was useful, I write about Math and ML weekly at Math Mindset (mathmindset.substack.com). It's free.
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